"The Qaim is My descendant, He lives the age of Abraham, hundred and twenty years. It is known about Him, then He disappears in the time and reappears in the form of a 32 years young boy, even a group of people return to Him. He fills the earth with justice and fairness, even as it will be filled with injustice and tyranny."

"The Qaim is My descendant, He lives the age of Abraham, hundred and twenty years."

The Biblical equivalent of this part of Hadith, is in Genesis 6:3:

Then the LORD said, “My Spirit shall not abide in man forever, for he is flesh: his days shall be 120 years.”

That is to say, the Perfect Man, who recieves the Spirit of God, lives 120 years.
And it is recorded in Traditions from Shia Imams, He is called Qaim, because, "He rises after He dies"

The historical parallel of this prophecy, is from year 1844, when the Bab, a descendent of Muhammad declaired He is the Qaim, and after ascension of the Bab, continued through the reappearence of the Spirit of Qaim in the person of Bahaullah, and after His passing, the ministry of Abdulbaha, and then Shoghi Effendi, until the year 1963, when the Universal House of Justice was established. When we count from 1844 to 1963, there are 120 years, in which the Faith of God was completely established. In Shia Traditions, it is recorded that, when Qaim rises, there will be 12 other Qaims after Him, and in fact, the Bab conferred the title of Qaim, upon His companion.

Then He said: "It is known about Him, then He disappears in the time and reappears in the form of a 32 years young boy"

The historical parallel of these narrations, is the declaration of the Bab, through which it was known He is the Qaim, and "the disappearence in the time" , is an allusion to His Martyrdom, and His reappearance in the form of a 32 years young boy, is an allusion to Bahaullah, who was 32 years old at the time of His disappearance, and after that the Babi community turned to Bahaullah for guidence.

And in the other Hadith He said " He stands among people, He is a 30 years old young man, He remains for 40 years."

The Bab was thirty in the last year of His revelation, and after Him, Bahaullah remained forty years.

The Báb, whose name was Ali-Muhammad, was born in Shiraz, on the first of Muharram, in the year 1235 A.H. He was the descendant of a house renowned for its nobility, which traced its origin to Muhammad Himself. His father, Siyyid Muhammad-Rida, as well as His mother, were descendants of the Prophet, and belonged to families of recognized standing. The date of His birth confirmed the truth of the saying attributed to the Imam Ali, the Commander of the Faithful: "I am two years younger than my Lord." The mystery of this utterance, however, remained unrevealed except to those who sought and recognized the truth of the new Revelation. It was He, the Báb, who, in His first, His most weighty and exalted Book, revealed this passage concerning Bahá'u'lláh: "O Thou Remnant of God! I have sacrificed Myself wholly for Thee; I have consented to be cursed for Thy sake; and have yearned for naught but martyrdom in the path of Thy love. Sufficient witness unto Me is God, the Exalted, the Protector, the Ancient of Days!" Shoghi Effendi : The Dawn-Breakers Part 1

The Báb, whose name was Siyyid Ali-Muhammad,[1] was born in the city of Shiraz, on the first day of Muharram, in the year 1235 A.H.[2] He belonged to a house which was renowned for its nobility and which traced its origin to Muhammad Himself. The date of His birth confirmed the truth of the prophecy traditionally attributed to the Imam Ali: "I am two years younger than my Lord." Twenty-five years, four months, and four days had elapsed since the day of His birth, when he declared His Mission. In His early childhood He lost His father, Siyyid Muhammad-Rida,[3] a man who was known throughout the province of Fars for his piety and virtue, and was held in high esteem and honour. Both His father and His mother were descendants of the Prophet, both were loved and respected by the people. He was reared by His maternal uncle, Haji Mirza Siyyid Ali, a martyr to the Faith, who placed Him, while still a child, under the care of a tutor named Shaykh Abid.[4] The Báb, though not inclined to study, submitted to His uncle's will and directions. Shoghi Effendi : The Dawn-Breakers Part 2

Imam Ja’far Sadiq (a.s.) said:
“The name of Imam Qaim (a.s.) will be announced on the 23rd night and he will reappear on the day of Ashura, on which Imam Husain (a.s.) was martyred.”

Imam Muhammad Baqir (a.s.) said: “As if I can see the Qaim (a.s.) on the day of Ashura, on Saturday standing between the Rukn and Maqam and Jibraeel is announcing before him: Allegiance is for Allah. Then he would fill the earth with justice and equity, like it would have been fraught with injustice and oppression.”

Recorded in Al-tabari, a Hadith attributed to Muhammad "The world is one of the weeks of the other world"

I.e. Friday being the sixth day, the Last Day of the Week in Islam.

There are two Qaims, One being from the lineage of Muhammad, who appears on Friday, and the other Qaim, appears on a Saturday, on the 23rd His call is raised, and on the Day of Ashura (i.e the 10th day) His mission begins.

The fulfilment of these prophecies according to history, came to pass with the Manifestation of the Bab and Bahaullah. The Bab's declaration, marked the expiration of the Day Six, from days of Adam (i.e. 6000 years), and Bahaullah's manifestation being the beginning of the next Day of God, i.e Saturday.
The 23rd night, is an allusion to 23 years after declaration of the Bab.
The mission of Bahaullah began 9 years after declaration of the Bab (i.e. the 10th year, alluded as Ashura) and His declaration to His close companions were after 19 years, but the Proclamation of Bahaullah openly to the world as a new Messenger of God began after 23 years, in Adrianople, in the year 1867.

Imam Ja’far Sadiq (a.s.) said:
“There will not be more than fifteen nights between the rising of the Qaim and the killing of the Pure Soul (Nafse Zakiyyah).”
This traditional report is mentioned in Ghaibat Shaykh and Irshad Mufeed.

In Bihar, it is recorded:

“Nafse Zakiyyah (the pure soul) is a young man from the Progeny of Muhammad (s.a.w.s.), his name is Muhammad bin Hasan, who would be killed without any crime and sin and when they slay, him they shall neither have any excuse in the heavens nor would they have any friend in the earth.
At that time the Almighty Allah will send the Qaim of Aale Muhammad with a group that in the view of the people would be softer than antimony. When they come out, the people will weep at their condition as they would think that they would very soon be eliminated at the hands of the enemies. However the Almighty Allah will conquer the easts and the wests of the earth for them.
Know that they are the true believers. Know that the best of the Jihads shall be in the last period of time.”

Quddus, whose name was Muhammad, and was from the progeny of Prophet Muhammad through Imam Hassan, was known among the Bab'is as fulfilment of the Pure Soul.

He was Martyred in the year, 1849, and Bahaullah declared His mission in year 1863. If we count from 1849 to 1863, there are 15 years, or 15 prophetic days.

Imam Ja’far Sadiq (a.s.) said:
“There will not be more than fifteen nights between the rising of the Qaim and the killing of the Pure Soul (Nafse Zakiyyah).”
This traditional report is mentioned in Ghaibat Shaykh and Irshad Mufeed.

In Bihar, it is recorded:

“Nafse Zakiyyah (the pure soul) is a young man from the Progeny of Muhammad (s.a.w.s.), his name is Muhammad bin Hasan, who would be killed without any crime and sin and when they slay, him they shall neither have any excuse in the heavens nor would they have any friend in the earth.
At that time the Almighty Allah will send the Qaim of Aale Muhammad with a group that in the view of the people would be softer than antimony. When they come out, the people will weep at their condition as they would think that they would very soon be eliminated at the hands of the enemies. However the Almighty Allah will conquer the easts and the wests of the earth for them.
Know that they are the true believers. Know that the best of the Jihads shall be in the last period of time.”

Quddus, whose name was Muhammad, and was from the progeny of Prophet Muhammad through Imam Hassan, was known among the Bab'is as fulfilment of the Pure Soul.

He was Martyred in the year, 1849, and Bahaullah declared His mission in year 1863. If we count from 1849 to 1863, there are 15 years, or 15 prophetic days.